(a) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels.
(b) Calculate the orbital period in each of these levels.

Explanation

Now `v_(n)=r_(n) omega`
`=r_(n)xx(2pi)/(T_(n))`
`:.T_(n)=(2pi r_(n))/(v_(n)) " "...(1)`
`:.` Time period n=1 orbit
`T_(1)=(2pir_(1))/(v_(1)) " "...(2)`
`=(2xx3.14xx0.53xx10^(-10))/(2.184xx10^(6))=(3.3284xx10^(-10))/(2.184xx10^(6))`
`=1.5239xx10^(-16)s=1.52xx10^(-16)s`
`rArr` Now `r_(n)=n^(2)r_(1) and v_(n)=(v_(1))/(n)`
`:.` From equation (1)
`T_(n)=(2pixxn^(2)r_(1))/(v_(1)//n)xxn^(3)((2pi r_(1))/(v_(1)))`
`:.T_(n)=n^(3)T_(1) [ :.` From equation (2)]
`rArr` Time period in n=2 orbit.
`T_(3)=(3)^(2)xxT_(1)`
`=27xx1.524xx10^(-16)`
`=4.114xx10^(-15)`
`=4.11xx10^(-15)s`